11.1 Triangles
120
C
A
D
B
E
F
Figure 11.5
11.2 The Parallel Postulate
121
We will prove that the sum of the angles of a triangle is a straight angle. In
the approach that we follow, the following partial result is essential.
Theorem 11.1.13.
The sum of any two angles of a triangle is less than 180
degrees.
Proof.
Consider an arbitrary triangle
ABC
as depicted in Figure 11.7, and ex-
tend the side
AB
beyond
A
as shown.
We will show that the sum of angles
CAB
and
ACB
is less than a straight angle.
A
F
B
M
C
D
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- Fall '08
- ROSENTHAL
- Math, Pythagorean Theorem, triangle, Euclidean geometry
